public class Roots extends java.lang.Object
Modified by: Joseph A. Huwaldt
| Constructor and Description |
|---|
Roots() |
| Modifier and Type | Method and Description |
|---|---|
static double |
aitken(Evaluatable1D eval,
double x,
double tol)
Find a root of a 1D equation using the Aitken method.
|
static int |
bracket(Evaluatable1D func,
double x1,
double x2,
int n,
double[] xb1,
double[] xb2)
Given a function,
func, defined on the interval x1 to
x2, this routine subdivides the interval into n equally
spaced segments, and searches for zero crossings of the function. |
static double |
findRoot1D(Evaluatable1D eval,
BracketRoot1D bracket,
double tol)
Find the root of a general 1D function
f(x) = 0 known to lie between
x1 and x2. |
static double |
findRoot1D(Evaluatable1D eval,
double x1,
double x2,
double tol)
Find the root of a general 1D function
f(x) = 0 known to lie between
x1 and x2. |
static boolean |
findRootsND(VectorFunction vecfunc,
double[] x,
int n)
Find the roots of a set of
N non-linear equations in N
variables. |
static void |
main(java.lang.String[] args)
Used to test out the methods in this class.
|
public Roots()
public static int bracket(Evaluatable1D func, double x1, double x2, int n, double[] xb1, double[] xb2) throws RootException
func, defined on the interval x1 to
x2, this routine subdivides the interval into n equally
spaced segments, and searches for zero crossings of the function. Brackets around
any zero crossings found are returned.func - The function that is being search for zero crossings.x1 - The start of the interval to be searched.x2 - The end of the interval to be searched.n - The number segments to divide the interval into.xb1 - Lower value of each bracketing pair found (number of pairs is returned
by function). The size of the array determines the maximum number of
bracketing pairs that will be found.xb2 - Upper value of each bracketing pair found (number of pairs is returned
by function). The size of this array must match the size of
xb1.RootException - if the supplied function can not accept
the interval provided.public static double findRoot1D(Evaluatable1D eval, BracketRoot1D bracket, double tol) throws RootException
f(x) = 0 known to lie between
x1 and x2. The root will be refined until it's accuracy
is tol.
Have your Evaluatable1D derivative() function return
Double.NaN when you want this routine to use Brent's method.
Newton-Raphson will be used if a derivative function is provided that returns
something other than Double.NaN. The function() method
will always be called before the derivative() method. The value
returned from the 1st call to the function() method is ignored.
eval - An evaluatable 1D function that returns the function value at x and
optionally returns the function derivative value (d(fx)/dx) at x. It
is guaranteed that "function()" will always be called before
"derivative()".bracket - The upper and lower bracket surrounding the root (assumed that root
lies inside the bracket).tol - The root will be refined until it's accuracy is better than this.RootException - if unable to find a root of the function.public static double findRoot1D(Evaluatable1D eval, double x1, double x2, double tol) throws RootException
f(x) = 0 known to lie between
x1 and x2. The root will be refined until it's accuracy
is tol.
Have your Evaluatable1D derivative() function return
Double.NaN when you want this routine to use Brent's method.
Newton-Raphson will be used if a derivative function is provided that returns
something other than Double.NaN. The function() method
will always be called before the derivative() method. The value
returned from the 1st call to the function() method is ignored.
eval - An evaluatable 1D function that returns the function value at x and
optionally returns the function derivative value (d(fx)/dx) at x. It is
guaranteed that "function()" will always be called before
"derivative()".x1 - The lower bracket surrounding the root (assumed that root lies between
x1 and x2).x2 - The upper bracket surrounding the root (assumed that root lies between
x1 and x2).tol - The root will be refined until it's accuracy is better than this.RootException - Unable to find a root of the function.public static double aitken(Evaluatable1D eval, double x, double tol) throws RootException
eval - An evaluatable 1D function that returns the function value at x and
optionally returns the function derivative value (d(fx)/dx) at x. This
method never calls "derivative()".x - A starting guess at the root value.tol - The root will be refined until it's accuracy is better than this.RootException - if unable to find a root of the function.public static boolean findRootsND(VectorFunction vecfunc, double[] x, int n) throws RootException
N non-linear equations in N
variables.
Uses a globally convergent Newton's method with either a Jacobian supplied by the VectorFunction or one computed by differencing.
Reference: Numerical Recipes in C, 2nd Edition, pg 386.
vecfunc - A VectorFunction that computes the values for each equation using
the input values in x[] and optionally the Jacobian.x - A pre-existing array that contains the initial guesses at the x
values. On completion, it will contain the roots of the equations.n - The number of equations to be solved (and the number of elements in
x.false if the routine completed normally or true
if the routine has converged to a local minimum of the "fmin" function. In
this case, try restarting from a different initial guess.RootException - Unable to find the roots of the functions.public static void main(java.lang.String[] args)
args - Command line arguments (not used).